Theory of quantum-electrodynamic flux tunneling in a superconducting ring with a Josephson weak link

Abstract

Previous work on the Josephson critical-current law and the flux-tunneling critical-voltage law (which used the Feynman path integral technique) is here extended in terms of the wave functions used in the quantum-electrodynamic circuit theory. The explicit wave function representations of the flux tunneling matrix elements are derived. The polarization charge matrix elements are determined by the dissipative features of the weak link and the flux tunneling is inhibited principally by the overlap integrals of the photon wave functions. It is shown that a strongly dissipative weak link has large-polarization-charge matrix elements which enhance flux tunneling. The physical picture of the tunneling event is the same from both the Feynman phase interference and the conventional wave function viewpoints.